Block Sparsity Promoting Algorithm for Efficient Construction of Cluster Expansion Models for Multicomponent Alloys.

Multicomponent alloys are gaining significance as drivers of technological breakthroughs especially in structural and energy storage materials. The vast configuration space of these materials prohibit computational modeling using first-principles based methods alone. The cluster expansion (CE) method is the most widely used tool for modeling configurational disorder in alloys. CE relies on machine learning algorithms to train Hamiltonians and uses first-principles calculated data as training sets. In this paper we present a new compressive sensing-based algorithm for the efficient construction of cluster expansion Hamiltonians of multicomponent alloys. Our algorithm constructs highly sparse and physically reasonable models from a carefully selected small training set of alloy structures. Compared to conventional fitting algorithms, the algorithm achieves more than 50 % reduction in the training set size. The resultant sparse models can sample the configuration space at least 3x faster. We demonstrate this algorithm on 4 different alloy systems, namely Ag-Au, Ag-Au-Cu, Ag-Au-Cu-Pd and (Ge,Sn)(S,Se,Te).The sparse cluster expansion models for these alloys can rapidly reproduce known ground state orderings and order-disorder transitions. Our method can truly enable high-throughput multicomponent alloy thermodynamics by reducing the cost associated with model construction and configuration sampling.